Spartak, who lead 1-0 from the first leg, opened the scoring in the 4th minute, Nikita Bazhenov slotting into an empty net after a good build up by the Muscovites.
However, the Czechs did not let their heads drop, and Rudolf Otepka equalized in the 24th minute, breaking well through a gap in the Spartak defense.
Spartak rode their luck in the second half, the Czechs going close to the winner on a number of occasions, hitting the woodwork three times, including twice in the dying minutes. However, Spartak held on somehow until the end of the match, their exhausted and relieved players dropping to the ground at the final whistle.
2005 UEFA Cup winners CSKA Moscow earlier made the group stages with a 1-0 win at home to Croatian minnows NK Slaven Koprivnica that came after a 2-1 victory in Croatia.
FC Moskva, trailing 2-1 after the first leg, kick off their away match against Danes FC Kobenhavn later on Thursday.
